Problem: Write the equation of a line that is parallel to ${y=6x+1}$ and that passes through the point ${(-7,1)}$.
Answer: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Slope of the given line: ${6}$ Slope of the parallel line: $C{6}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{6}$ and pass through the point ${(-7,1)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{1} &= C{6}(x-{(-7)})\\\\\\ y-1 &= C{6}x +42 \\\\\\ y &= C{6}x {+43} \end{aligned}$ Answer The equation of the parallel line is $y = C{6}x {+43}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$